C/C++ – Page 7 – Numerical Explorations

Another Matrix Cipher by James Pate Williams, Jr. BA, BS, MSwE, PhD

This is perhaps an improvement on the matrix cipher of a previous blog post of mine. In that post I introduced a matrix cipher whose keys were generated by selection of a seed such that 1 <= seed <= 2147483647, a number N such that 2 <= N <= 1000, and plaintext of length n such that 1 <= n <= N -1.

This matrix cipher relies on the ANSI X9.17 pseudorandom number generator (PRNG) of 5.11 Algorithm of the Handbook of Applied Cryptography by Alfred J. Menezes, et al. The PRNG uses triple-DES with a potential 168-bit (56 * 3 = 168) key space using E-D-E (Encryption key 1 – Decryption key 2 – Encryption key 3). Also, a 64-bit date related number and a 64-bit random seed are needed to initialize the PRNG.

The key space for the algorithm is (168 + 128) bits which is 296 bits. Here is the encryption and decryption of the ASCII ten characters string “ATTACK NOW”.

New Matrix Cipher 0

New Matrix Cipher 1

New Matrix Cipher 2

New Matrix Cipher 3

New Matrix Cipher 4

The first step in the cryptanalysis of this cipher would be to determine the modulus of the matrix and vector calculations N. I don’t know how many ciphertexts would be necessary to perform this task. From the preceding known ciphertext we find that N is at least 991. From traffic analysis we may have determined that the maximum value of N is 1000. That means would we only need to try 10 values of N.

Two of My Many Sorting Algorithms Implementations by James Pate Williams, Jr. BA, BS, MSwE, PhD

A recurring theme in my life has been to implement and re-implement the sorting algorithms found in Harold Lorin’s treatise Sorting and Sort Systems and Thomas H. Corman et al.’s Algorithms. I purchased a copy of Lorin’s book in the summer of 1979 and Corman’s textbook in 1999 or 2000. This has been good exercise in translating from one computer language to a later and greater newer computer language. I began in BASIC and FORTRAN IV and transitioned to C, C++, C#, Common LISP, Java, Modula-2, Pascal, and Scheme in alphabetic not chronological order. In this blog we cover two C# applications, one from October 26, 2010, named Sorting Comparisons and the other from January 17, 2015, with the moniker Sorting.

In the Sorting Comparisons application, we compare the sorting algorithms: Heap Sort, Quick Sort, and Singleton’s Sort. The first two algorithms are from the Algorithms tome and Singleton’s Sort is from Lorin’s treatment. These are some of the fastest general purpose sorting algorithms available in my particular arsenal.

Sorting Comparisons Test All 16 Sorting Comparisons Time All 1000